Critical dwell time of switched linear systems

In this paper, we consider the relation between the switching dwell time and the stabilization of switched linear control systems. First of all, a concept of critical dwell time is given for switched linear systems without control inputs, and the critical dwell time is taken as an arbitrary given positive constant for a switched linear control systems with controllable switching models. Secondly, when a switched linear system has many stabilizable switching models, the problem of stabilization of the overall system is considered. An on-line feedback control is designed such that the overall system is asymptotically stabilizable under switching laws which depend only on those of uncontrollable subsystems of the switching models. Finally, when a switched system is partially controllable （While some switching models are probably unstabilizable）, an on-line feedback control and a cyclic switching strategy are designed such that the overall system is asymptotically stabilizable if all switching models of this uncontrollable subsystems are asymptotically stable. In addition, algorithms for designing switching laws and controls are presented.

Asynchronous Observer Design for Switched Linear Systems: A Tube-Based Approach

This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances.Sufficient stability conditions of the nominal observer error system under mode-dependent persistent dwell-time(MPDT)switching are first established. Taking the disturbances into account, a novel asynchronous MPDT robust positive invariant(RPI) set and an asynchronous MPDT generalized RPI(GRPI)set are determined for the difference system between the nominal and disturbed observer error systems. Further, the global uniform asymptotical stability of the observer error system is established in the sense of converging to the asynchronous MPDT GRPI set, i.e., the cross section of the tube of the observer error system. Finally, the proposed results are validated on a space robot manipulator example.

Stabilization of Slowly Varying Switched Linear Systems

The stabilization problem of systems that switch among a finite set of slowly varying linear systems with arbitrary switching frequency is discussed.It is shown that if the entries of the pointwise stabilizing feedback gain matrix are continuously differentiable functions of the entries of the system coefficient matrices,then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small.

State observers of quasi-reversible discrete-time switched linear systems

This work addresses observer design for the general class of quasi-reversible discrete-time switched linear systems.Under the mild assumption that the switched system is observable,we present constructive approaches to design state observers to estimate the state.Two types of observers are designed:one is with full order and the other is with reduced order,both could reconstruct the system state in finite times.A numerical example is presented to illustrate the effectiveness of the proposed approaches.

Approximating the Spectral Abscissa for Switched Linear Systems via Coordinate Transformations

In this paper,an approach of square coordinate transformation is proposed to approximate the spectral abscissa for continuous-time switched linear systems.By applying elementary transformations iteratively,a series of minimums of least μ1 matrix set measures are obtained,which are utilized to approximate the spectral abscissa of the switched system.The approach is developed into tractable numerical algorithms that provide upper bound estimates of the spectral abscissa.Numerical simulations show the effectiveness of the proposed method.

Robust observer-driven switching stabilization of switched linear systems

In this work, we study the robust observer-driven switching stabilization problem of switched linear sys- tems. Under the condition that each subsystem is completely observable, with the observer-driven switching law which makes the system exponentially stable for the nominal system, we prove that the overall system is robust against structural/switching perturbations and is input/output to state stable for unstructural perturbations.

Design of two-layer switching rule for stabilization of switched linear systems with mismatched switching

A two-layer switching architecture and a two-layer switching rule for stabilization of switched linear control systems are proposed, under which the mismatched switching between switched systems and their candidate hybrid controllers can be allowed. In the low layer, a state-dependent switching rule with a dwell time constraint to exponentially stabilize switched linear systems is given; in the high layer, supervisory conditions on the mismatched switching frequency and the mismatched switching ratio are presented, under which the closed-loop switched system is still exponentially stable in case of the candidate controller switches delay with respect to the subsystems. Different from the traditional switching rule, the two-layer switching architecture and switching rule have robustness, which in some extend permit mismatched switching between switched subsystems and their candidate controllers.

Delay-dependent stability and stabilization of a class of linear switched time-varying delay systems

The stability and stabilization of a class of linear switched time-varying delay systems are investigated. A piecewise quadratic Lyapunov function （PWQLF） is constructed and is used to obtain the stability conditions based on the linear matrix inequalities （LMIs）. The stabilizing controller for this class of system is then designed and the solution of the desired controller can be obtained by a cone complementary linearization algorithm. Numerical examples are provided to illustrate the less conservativeness of the new stability and the validity of the controller design procedures.

Robust H_∞ output feedback controller design for linear uncertain discrete-time switched systems via state reset

This paper studies the problem of robust H∞ output feedback controller via state-reset for linear uncertain discrete-time switched systems. Using multiple Lyapunov functions,we address an output feedback controller under arbitrary switching signals,in which an H∞ performance is required. The condition is shown in the form of linear matrix inequalities (LMI). Finally,a numerical example shows the feasibility of the designed controller and illustrates that the new sufficient condition has lower conservation and more optimized H∞ tfperformance.

Delay-dependent robust H∞ control for a class of uncertain switched systems with time delay

For linear switched system with both parameter uncertainties and time delay, a delay-dependent sufficient condition for the existence of a new robust H∞ feedback controller was formulated in nonlinear matrix inequalities solvable by an LMI-based iterative algorithm. Compared with the conventional state-feedback controller, the proposed controller can achieve better robust control performance since the delayed state is utilized as additional feedback information and the parameters of the proposed controllers are changed synchronously with the dynamical characteristic of the system. This design method was also extended to the case where only delayed state is available for the controller. The example of balancing an inverted pendulum on a cart demonstrates the effectiveness and applicability of the proposed design methods.

H∞ Tracking Control for Switched LPV Systems With an Application to Aero-Engines

This paper focuses on the H_∞ model reference tracking control for a switched linear parameter-varying(LPV)model representing an aero-engine. The switched LPV aeroengine model is built based on a family of linearized models.Multiple parameter-dependent Lyapunov functions technique is used to design a tracking control law for the desirable H_∞ tracking performance. A control synthesis condition is formulated in terms of the solvability of a matrix optimization problem.Simulation result on the aero-engine model shows the feasibility and validity of the switching tracking control scheme.

An Improved Method for Approximating the Infinite-Horizon Value Function of the Discrete-Time Switched LQR Problem

This paper considers the problem of approximating the infinite-horizon value function of the discrete-time switched LQR problem.In particular,the authors propose a new value iteration method to generate a sequence of monotonically decreasing functions that converges exponentially to the value function.This method facilitates us to use coarse approximations resulting from faster but less accurate algorithms for further value iteration,and thus,the proposed approach is capable of achieving a better approximation for a given computation time compared with the existing methods.Three numerical examples are presented in this paper to illustrate the effectiveness of the proposed method.

Exponential L1 Filtering of Networked Linear Switched Systems:An Event-Triggered Approach

The issues of event-triggered exponential L1 filtering are studied for a class of networked linear switched systems.An event-triggered mechanism is proposed to enhance resource utilization in transmission,and save the communication cost of systems as well.Then,the filtering error system is reconstructed as a switched delay system with bounded disturbance through the input delay system approach.By resorting to the Lyapunov-Krasovskii functional approach and the average dwell time(ADT)technique,some interesting results are derived to guarantee the exponential stability with a prescribed L1 disturbance rejection level.Further,an event-triggered exponential L1 filter is designed via solving a set of feasible linear matrix inequalities(LMIs).Finally,the efficiency of the proposed results is verified through a numerical example and a PWM-driven boost converter circuit system.

Convergence analysis of a least squared algorithm of linear switched identification

A novel identification algorithm is proposed to deal with the modelling issues of linear switched systems under the switching modes being unknown.The main contributions of this paper embody the following aspects:(1)for simplifying the identification problems,the label functions are proposed to replace the switching states of the modes;(2)The recursive least square algorithm is used to identify the system parameters,and the convergence performance of the proposed algorithm is studied.By using convergence analysis,the parameter estimation error can converge to zero point when the input signals satisfy persistent excited conditions and the total time of mode mismatch is limited.Finally,the effectiveness of the proposed method is verified by a simulation example.

Smooth tracking control for conversion mode of a tilt-rotor aircraft with switching modeling

This paper investigates the state-tracking control problem in conversion mode of a tilt-rotor aircraft with a switching modeling method and a smooth interpolation technique.Based on the nonlinear model of the conversion mode,a switched linear model is developed by using the Jacobian linearization method and designing the switching signal based on the mast angle.Furthermore,an ℋ_(∞) state-tracking control scheme is designed to deal with the conversion mode control issue.Moreover,instead of limiting the amplitude of control inputs,a smooth interpolation method is developed to create bumpless performance.Finally,the XV-15 tilt-rotor aircraft is chosen as a prototype to illustrate the effectiveness of this developed control method.